A man is standing on the top of the building, 30m height. He drops a ball from the top, at a same time another man standing on the ground floor, throwing a ball at a initial speed of 30m/s. In what time two balls will collide each other.

Here the logic is simple, a freely falling body in the earth will be having acceleration of 9.8m/s. The initial velocity of the ball which the man drops from the top of the building will be zero, but the initial velocity of the ball which is through from the ground floor will be 30m/s. The balls are moving opposite direction. Equate the poison of both balls, because both balls are colliding each other after some time.

From the newtons law of motion, three equations can be derived.

V = U + AT -------------------------------------- (1)

S = UT + (½) AT2 + S0. ---------------------------------------(2)

V2 = U2 + 2AS + ---------------------------------------(3)

where.

V = Velocity of an object.
U = Initial velocity of an object.
S = Distance traveled by the object.
T = Time period of the object.
A = Acceleration of the object.
S0 = initial distance

1) For this problem, it doesn't matter what the strength of the gravity field is. It will still take 1 sec for collision on the moon, Mars, Jupiter, or no gravity at all.

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Note also the building height and lower ball launch velocity are not vital, so long as they are of equal magnitude. In other words, one building height per second for the lower ball regardless of building height. Meters, miles, astronomical units, doesn't much matter until we approach light-seconds.